Abstract

We evaluate the effect of finite aperture gratings on the spectral and efficiency characteristics of guided-mode resonance filters. A simple analytical model based on the attenuation properties of the waveguide and a fixed length of the grating aperture is developed. The results from this model are in good agreement with experimental filters formed with subwavelength period photoresist gratings and solgel waveguides.

© 2000 Optical Society of America

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    [CrossRef]
  6. M. Nevière, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
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    [CrossRef]
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    [CrossRef]
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  14. J. A. Cox, R. A. Morgan, R. Wilke, C. Ford, “Guided-mode resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
    [CrossRef]
  15. I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
    [CrossRef]
  16. R. Magnusson, S. S. Wang, “Characteristics of waveguide-grating filters: plane wave and Gaussian beam illumination,” in IEEE Lasers and Electro-Optics Society 1993 Annual Meeting Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 157–158.
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  22. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
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1999 (1)

1998 (3)

1997 (1)

1996 (2)

1995 (5)

1990 (1)

1989 (1)

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

1986 (2)

E. Popov, L. Mashev, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 16, 1558–1559 (1986).
[CrossRef]

1985 (1)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

1979 (1)

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

1965 (1)

Avrutskii, I. A.

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 16, 1558–1559 (1986).
[CrossRef]

Avrutsky, I. A.

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

Bagby, J. S.

Boye, R. R.

Brazas, J. C.

Brundett, D. L.

Cox, J. A.

J. A. Cox, R. A. Morgan, R. Wilke, C. Ford, “Guided-mode resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Engel, H.

Ford, C.

J. A. Cox, R. A. Morgan, R. Wilke, C. Ford, “Guided-mode resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Friesem, A. A.

Gale, M. T.

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagen, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

Gaylord, T. K.

Giovannini, H.

Glasberg, S.

Glytis, E. N.

Grann, E. B.

Hessel, A.

Knop, K.

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagen, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

Kostuk, R. K.

Lemarchand, F.

Li, L.

Liu, Z. S.

Magnusson, R.

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, “Characteristics of waveguide-grating filters: plane wave and Gaussian beam illumination,” in IEEE Lasers and Electro-Optics Society 1993 Annual Meeting Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 157–158.

Mashev, L.

E. Popov, L. Mashev, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Moharam, M. G.

Morf, R.

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagen, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

Morgan, R. A.

J. A. Cox, R. A. Morgan, R. Wilke, C. Ford, “Guided-mode resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Morris, G. M.

Nevière, M.

Noponen, E.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Oliner, A. A.

Peng, S.

Pommet, D. A.

Popov, E.

M. Nevière, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

E. Popov, L. Mashev, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Reinisch, R.

Rosenblatt, D.

Saarinen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Sentenac, A.

Sharon, A.

Shin, D.

Steingrueber, R.

Sychugov, V. A.

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 16, 1558–1559 (1986).
[CrossRef]

Tibuleac, S.

Turunen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Vincent, P.

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Wang, S. S.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, “Characteristics of waveguide-grating filters: plane wave and Gaussian beam illumination,” in IEEE Lasers and Electro-Optics Society 1993 Annual Meeting Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 157–158.

Weber, H. G.

Wilke, R.

J. A. Cox, R. A. Morgan, R. Wilke, C. Ford, “Guided-mode resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Young, P. P.

Ziolkowski, R. W.

Appl. Opt. (3)

Appl. Phys. (1)

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

J. Mod. Opt. (1)

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Acta (1)

E. Popov, L. Mashev, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Opt. Commun. (1)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Opt. Eng. (1)

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Opt. Lett. (5)

Sov. J. Quantum Electron. (1)

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 16, 1558–1559 (1986).
[CrossRef]

Other (3)

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagen, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, “Characteristics of waveguide-grating filters: plane wave and Gaussian beam illumination,” in IEEE Lasers and Electro-Optics Society 1993 Annual Meeting Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 157–158.

J. A. Cox, R. A. Morgan, R. Wilke, C. Ford, “Guided-mode resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Diagram showing the general form of the GMRF’s fabricated for study. (a) Each slide was fabricated with five grating lengths. The refractive indices for the photoresist, solgel, and fused silica were 1.62, 1.5, and 1.46, respectively. (b) A closeup of the GMRF geometry. The grating was modeled as a square wave.

Fig. 2
Fig. 2

Laboratory arrangement for measuring the spectral width of the GMRF’s resonance in reflection. The samples were typically positioned at approximately 1 deg to provide a resonance at 673 nm.

Fig. 3
Fig. 3

Experimental measurement of the spectral resonance width is compared with the model based on Eq. (6) and approximation (7). The expected peak widths from an infinite grating were found by use of RCWA and are shown by the constant lines.

Fig. 4
Fig. 4

Peak efficiency of the GMRF’s was also effected by the length of the grating.

Fig. 5
Fig. 5

Example resonance measurements from grating 1. The actual grating lengths were shorter than the lengths denoted here. 5 mm = 4.60 mm, 4 mm = 3.67 mm, 2 mm = 1.78 mm, and 1 mm = 0.798 mm. The widths of these peaks and their peak values are shown as diamonds in Figs. 3 and 4, respectively.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Enfx=A exp-αx,
Effθ, λ=A|α|11+j2π θ-θ0|α|λ,
Enfx=A exp-αxrectxa,
rectxa=1,when |x|<a/20,when |x|a/2.
Effθ, λ=A1-exp-αa|α|11+j2π θ-θ0|α|λ* sincaλθ-θ0.
δθ=λα2πnc cos θ02+0.443λanc cos θ0/e21/2,
δλδθncΛ,
Speak=Aα1-exp-αa.
Rpeak=1-exp-αa.
Speakmeasured=A1-exp-αaea cos θ0e+A2,

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